15 ms·
Mathematicians solve decades-old classification problem
- paulpauper 5y agoseems like unsolved problems are being solved at a breakneck speed https://www.google.com/search?q=site%3Ahttps%3A%2F%2Fwww.quantamagazine.org%2F+solve+problem&source=hp&ei=pwQMYbmiEsTc-gTQhZP4Ag&iflsig=AINFCbYAAAAAYQwSt7pzVhxvpt6X1XBNT0UeVCJiholZ&oq=site%3Ahttps%3A%2F%2Fwww.quantamagazine.org%2F+solve+problem https://www.google.com/search?q=site%3Ahttps%3A%2F%2Fwww.qua...
- magneticnorth 5y agoI love this series of Quanta's. They have truly excellent coverage of real, modern mathematics results of the type that are very hard to explain outside of their own field. Speaking as a former mathematician, I don't think problems are being solved any faster lately, but we hear about it more outside of academia because this is something that Quanta has started covering. As an example, you could look only at Saharon Shelah, one of the co-authors of this result and a giant in the fields of model theory and set theory. He has spent a career settling long-standing open problems, including Whitehead's problem and Morley's problem. Until this Quanta series, Shelah's work didn't get much coverage outside mathematics as far as I know, but results of this caliber are not atypical for him. https://en.wikipedia.org/wiki/Saharon_Shelah#Academic_career https://en.wikipedia.org/wiki/Saharon_Shelah#Academic_career
- jjgreen 5y agoShelah's productivity is astonishing, but he uses the worst notation possible, his preprints are practically unreadable as a result (not that I'm clever enough to understand them).
- tux3 5y agoThat begs the question of whether the unorthodox notation is a catalyzer for the results he gets, just a coincidence, or if just thinking differently in general is the reason for both. =)
- mhh__ 5y agoI think notation is completely misunderstood by some fields, and that physics in particular really shows the benefits of it (i.e. With tensors and feynman diagrams we can nearly stop ourselves from writing down the wrong answer through notation), but academics are just as idiosyncratic as everyone else so I'd guess something more human.
- Bayart 5y agoI've got terrible mathematical education, but Feynman diagrams are something even a clown like myself can easily wrap his head around. They're really an exceedingly clever device, end "clever" doesn't do it justice.
- mhh__ 5y agoThey don't even have to be Feynman diagrams - theoretical (rather than mathematical) physicists are usually pretty lazy. We make up notation for us rather than the reader. Mathematicians, I find, are a lot worse but still bearable. Engineers though, oh boy, seem to actively enjoy using notation to obscure the material in the books I have read.
- dmix 5y agoI bought ~5 different kindle books on logic as a prerequisite for understanding another book I originally bought on Probability Theory (E. T. Jaynes). Every logic book I bought used a different notation and none of them matched the notation used in the book I wanted to read either, which is how I ended up with 5 of them. You'd think something as straight forward as (boolean) logic would converge on a standard notation. But I'm not familiar with the mathematics field to really criticize this. Regardless I found it to be a large barrier-to-entry which over complicated something when I was hoping to find direct analogies not needing constant 'translation'.
- sorokod 5y agoIt is said about Saharon Shelah that colleagues are reluctant to share research problems with him since he solves them on the spot.
- OscarCunningham 5y agoCan you give an example paper? I want to see what you mean.
- jjgreen 5y agoPicked pretty-much at random, but typical of what I mean: https://arxiv.org/pdf/1802.01137.pdf https://arxiv.org/pdf/1802.01137.pdf The use of the filled club ♣ makes the whole thing look like it's been sneezed on by someone who's just come off a shift in a coal-mine. There are 1087 published research papers here if you'd like to browse ... https://shelah.logic.at/paper-list/ https://shelah.logic.at/paper-list/
- Koshkin 5y agoI wonder if computers have something to do with this.
- random_upvoter 5y agoI'm reminded how Newton invented modern physics after spending a year(?) in seclusion because of the pest raging in London and I wonder if something similar has been going on with the Covid lockdowns.
- deleted 5y ago[deleted]
- m3kw9 5y agoCan this be used to classify molecules, which also have near infinite chemical spaces?
- ducttapecrown 5y agoNo.
- timestampgalore 5y agocan't wait till this problem has to be solved within 20 mins in a tech interview
- hutrdvnj 5y ago... and you passed it, but then they tell you that you missed the job criteria, because you don't have 10 years kubernetes experience, which is a hard requirement
- spywaregorilla 5y agoWhat is the day to day of someone trying to solve potentially unsolveable problems? How much of it is just starting blankly at a chalkboard?
- ellis-bell 5y agoa huge part of it is trying to solve / formulate easier versions of the problem, or problems that are similar or related to the original problem. Or making some stronger assumptions to get rid of the clutter / all of the moving variables and distill it down to the smallest form a human brain can handle! For many of the "huge" unsolved problems, there tends to be a program of "dominos" or "ledges" you hope to work on in some order that will make the original problem fall. that way you don't just meander idolly from day to day, but instead gain some intuition for the central problem (and of course have publishable work to appease the grant gods / the university). trying to code up some of the work to experiment is also useful, but that can be a research problem of its own :-)
- tzs 5y agoJulia Robinson [1], who played a crucial role in resolving Hilbert's Tenth Problem, was once asked by the personnel department at her university to submit a description of what she did. She gave them a description of her typical work week: Monday: Try to prove theorem Tuesday: Try to prove theorem Wednesday: Try to prove theorem Thursday: Try to prove theorem Friday: Theorem false [1] https://en.wikipedia.org/wiki/Julia_Robinson https://en.wikipedia.org/wiki/Julia_Robinson
- eigenket 5y agoA good start is to try easier problems that will hopefully provide some insight into the hard problem. I.e. if you have some theorem you want to prove about all matrices of a certain form then do it for 2x2 and 3x3 matrices first or something. Straight up numerical examples help me a lot as well, so a first approach is to write some code that generates specific cases I can play around with. Obviously the usefulness of this varies a lot depending on the field and the problem. Personally I really like coming up with counterexamples to stuff, i.e. if someone has an idea for something they think is true I'm really good at coming up with random examples that break it, so if I'm trying to prove something occasionally I take a break and try to work out what a counterexample would look like and this often provides insight into why counterexamples can't exist.
- FredPret 5y ago…turns out that dress is white and gold
- locao 5y agoSo THAT'S why Brazil is quickly destroying the Amazon. No forest, no need to classify species.
- raister 5y agoMany 'external' actors are actually destroying the Amazon: Brazil's incompetence whilst voting (putting a crazy in charge); USA's inability to embargo Brazil if it keeps devastating the forest; Amazon is not located 'just at' Brazil, there are at least 5 other countries in the region; lack of international preoccupation with the forest; I could go on and on and on... Edit: 'on' to 'in' charge.
- locao 5y agoSure, I should have said "the crazy in charge", not Brazil itself. And, although you're right about Amazon existing beyond Brazil, its Brazilian territory that is being devastated right now. USA is not the world regulator, but I agree that an worldwide embargo is fully justified in this case. Finally, it was just a joke about the example the author used in the article.
- klysm 5y agoThis seems related to computational complexity theory, but in a more ‘structural’ notion as it deals not with the algorithms that are doing the comparisons but whether or not objects even have attributes you can differentiate by.